Nilpotency, Solvability and Frattini Theory for Poisson algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916712503312384 |
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| author | Towers, David A. |
| author_facet | Towers, David A. |
| contents | This paper shows that a Poisson algebra is nilpotent if and only if it is both associative and Lie nilpotent and examines various properties of the nilradical and the solvable radical. It introduces a basic Frattini theory for dialgebras and then investigates a more detailed theory for Poisoon algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20638 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nilpotency, Solvability and Frattini Theory for Poisson algebras Towers, David A. Rings and Algebras Algebraic Geometry 17A32, 17B05, 17B20, 17B30, 17B50 This paper shows that a Poisson algebra is nilpotent if and only if it is both associative and Lie nilpotent and examines various properties of the nilradical and the solvable radical. It introduces a basic Frattini theory for dialgebras and then investigates a more detailed theory for Poisoon algebras. |
| title | Nilpotency, Solvability and Frattini Theory for Poisson algebras |
| topic | Rings and Algebras Algebraic Geometry 17A32, 17B05, 17B20, 17B30, 17B50 |
| url | https://arxiv.org/abs/2504.20638 |